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Given diploma thesis deals with the systematic method for analysis of performance loss when using simplified model predictive control formulations. Aim of this thesis is to analyze and compare system response using model predictive control (MPC) implemented on a reference and simplified controller. To find the maximum difference between these controllers and to solve this problem we use bilevel programming. The main drawback of MPC is in increasing of the complexity in both cases (off-line and on-line) as the size of the system model grows larger as well as the control horizon and the number of constraints are increasing. One part of the thesis deals with introduction into MPC and with techniques how to make MPC faster. There are some techniques as model reduction, move blocking, changing the prediction horizon and changing the sampling time, which can be used for simplify MPC problem that makes the optimization problem easier to solve and thus make MPC faster. Using the model reduction to reduce model state variables is important, e.g. the more states variables model contains, the more complex the regulator must be. This fact is very important especially for explicit MPC. Using input blocking we fix the inputs to be constant and using delta-input blocking we fix the difference between two consecutive control inputs to be constant over a certain number of time-steps which reduce degrees of freedom. Reducing prediction horizon we make MPC problem easier to solve. As an example of controlling a typical chemical plant we here consider MPC for a distillation column. Using a bilevel program and model of distillation column we compare these simplify techniques and we focus on the connection between control performance and computational effort. Finally, results are compared and the best way of simplification for our example of plant is found, which turns out to be delta input blocking.